An equation devised by astronomer and SETI researcher Frank Drake to estimate the number of
civilizations in our Galaxy that might be detectable across interstellar
distances. There are several extant variations of the equation, but the original form was as follows:
N = R
The main body of the equation computes the number of technologically advanced civilizations
likely to come into existence in a single year. The final 'L' factor estimates these
civilizations' likely lifespans, and so approximates the total number of such civilizations
that might be in existence at any particular point. With the exception of R and fp,
all of these factors are highly speculative, but it is possible to at least produce a range of estimates,
and this process can throw up some interesting considerations.
The annual rate of stellar formation within the
Galaxy. We can place this figure fairly safely
in the range 10 to 20, with observational evidence favouring the higher figure.
The fraction of these stars that form planetary
systems. Less than a decade ago, we could do no more than guess at this figure. Since 1995, a wealth of data has become
available showing that extrasolar planets not only exist, but are a fairly common phenomenon.
A widely accepted value for fp is 0.2.
The expression R fp, then, is calculable with at least a fair degree of accuracy:
20 x 0.2, which gives a value of four planetary systems coming into existence each year in our
Galaxy. The next four factors attempt to calculate how many technological civilizations will
develop within these systems. In each case, a highly optimistic and pessimistic figure is suggested, with the aim of at least defining
a likely range of values for N.
The average number of planets in a system that are suitable for the development of
life. This is a particularly difficult figure to estimate, since the conditions needed for
life to start are not known with any certainty. We might perhaps base the value on locations where
amino acids are likely to have emerged spontaneously. For our Solar System,
at least, this results in a surprisingly large number. Earth is a certainty, of course, but an
argument could be made for at least two of Jupiter's moons,
and even Jupiter's own atmosphere. Saturn's
moon Titan seems to have all the necessary ingredients, and in the distant past
Mars supported an ocean environment, making it a candidate too. For our own
Solar System, this gives an estimate of six candidates. Note that we aren't
concerned with whether life actually does exist in all these locations - it almost certainly
does not - the value describes locations where life could appear.
The value of six seems intuitively to be more than a trifle optimisitic: it may very well be that a far more complex
array of factors is needed for life to be possible, though it's almost impossible to
define what these factors might be. As a pessimistic offset to the high value of six, a figure such a 0.1 seems at least plausible
(that is, a planet where conditions are right for life to
emerge appears only once in every ten planetary systems).
The fraction of planets where life might appear
on which it actually does. Again, there is very little basis for a calculation here. Using the possibility of amino acid
formation to calculate ne, though, at least gives us some basis for estimating
fl. We know that, under the right conditions, amino acids will form spontaneously from common
chemicals, and will proceed to organise themselves into molecular chains known as peptides. Depending on the particular amino
acids in the chain, even relatively simple peptides will demonstrate interesting properties, including - highly relevant to the
question of life - the ability to replicate themselves. The available evidence seems to point quite strongly towards this kind of
process taking place on the early Earth, but what is far less clearly understood at present is
how these self-replicating molecules advanced to the point where they could realistically be referred to as
It may be that the development of self-replicating chains of amino acids leads almost inevitably to more and more
complex systems, and that once the process has started life will emerge all but automatically.
If this is true, then fl is close to 1 - we'll use a figure of 0.95 as an optimistic estimate.
For all we know, though, the next step in the process is very far from automatic. It may be that the young
Earth with its cargo of self-replicators experienced some highly unusual event (the arrival of a
meteorite carrying just the right chemicals, for example) that triggered its development into true
life. If this pessimistic view is correct, then the appearance of
life might be extremely rare, though it's impossible to guess how rare without knowing the
nature of the 'trigger'. We might estimate a pessimistic fl at
0.001 - one chance in a thousand.
It should be noted that these guesses can only take into account what little we know of the development of
life on Earth. For all we know, the amino acid
route might be unusual in the Galaxy as a whole, with most
life emerging by some process entirely unknown to us.
The fraction of those planets on which life appears where it
evolves into an intelligent form. This seems to be a fairly simple question at first sight, but the more closely we look at the idea,
the more difficult 'intelligence' is to define. Intuitively, we tend to define humans as the only
life on Earth that can claim intelligence, but to imagine
intelligence beyond the Earth we need to consider the matter from a non-human perspective, and
that's very difficult to achieve.
A hypothetical non-human observer might consider for example the ventilated, air-conditied cities of termites, the
agricultural activities of certain ants, the immensely complex communication patterns of cuttlefish,
the social structures of dolphin communities, or the inventive tool-making and cultural diversity of chimpanzees.
The value of fi depends on how broadly we define 'intelligence'. If we
allow some or all of these examples of non-human intelligence, then we can say that it has evolved
independently on several occasions, and therefore fi must be high, at say 0.75.
Alternatively, if we take humanity as the benchmark, then intelligence has appeared just once in the
history of life on Earth, and must be a rare commodity.
Perhaps the path of evolution of life on Earth is somehow unusual in the
Galaxy as a whole. For example, the existence and sudden disappearance of the dinosaurs
certainly had a significant impact on the development of mammals and ultimately humans. If evolutionary 'U-turns' like this are
fairly rare events, then it may be that fi is quite low: 0.1, for example.
The fraction of intelligent lifeforms that develop the capacity for interstellar communication. This figure
is extremely difficult to estimate, but even on the most optimistic assessment it would seem to be quite low.
Even if we admit all the candidates for intelligence listed above, very little potential emerges. The
'technologies' of termites and ants are instinctive in nature, and driven by evolutionary necessity: it's
hard to see how this could lead to radio telescopy. Dolphins, however intelligent they may be, have no means
of manipulating their environment, and so any kind of dolphin technology is out of the question.
To have any hope of developing to this level requires a capacity for tool use and an adaptive, inventive
intelligence. Among all of Earth's life, this is restricted to
one particular group of animals, the apes, and of these only humans have come close to the level of technology required to
contact other civilizations. On this basis, even an optimistic estimate would for fc
would be low - say 0.1 or one-in-ten. A pessimistic estimate would be much lower still, at about
0.001 or one-in-one-hundred.
We're now at the point where some calculations are possible. Taking the optimistic estimates throughout
the above, we can compute that life will emerge somewhere in our Galaxy 22.8 times a year
(about once every sixteen days), and that 1.71 communicating civilizations will develop in the same period. These are remarkable
figures - they suggest that a civilization comparable to our own will appear, somewhere among the
the stars of the Milky Way Galaxy, every seven months. These figures represent an
upper limit - the best possible scenario.
The pessimistic calculation, as expected, results in much reduced expectations. According to these
estimates, the Galaxy will see
life appear just once every 2,500 years. The annual rate for
the appearance of intelligent technological civilizations is even lower: 0.0000004. On
this basis, such civilizations will appear at intervals of about 2½ million years. This represents
something like a minimum figure, and although 2½ million years might seem like a long time,
it is still an extraordinary result. That's especially true when we consider the final factor
in the Drake Equation, L.
The Drake Equation was formulated in 1961, at a time of intense nuclear confrontation between the
superpowers. The Cuban Missile Crisis was just months away, and the possibility that humanity might
extinguish itself seemed very real indeed. L is something of a product of these times - it
estimates the lifespan of a civilization, or at least the time during which that civilization
is capable of communication. It effectively presumes that any civilization must
come to an end eventually.
Now that we live in more optimistic times, L might seem just a little too negative, since there now seems
no immediate risk of mankind's destruction. There are undoubtedly long-term threats to
life on Earth, environmental and astronomical, but
these can be understood and prepared for. From this more positive perspective, a sufficiently developed civilization might
well enjoy the prospect of an indefinite existence. If we follow this line, L becomes equivalent a term we might perhaps
refer to as LG: the lifespan not of an individual civilization, but of the
Galaxy as a whole. (This is not to dismiss the original factor L, of course: we'll
return to this term shortly).
The value of LG can be estimated with some confidence. We might assign a conservative estimate of
about 10,000,000,000 years (though in fact the true figure might be somewhat higher than this). We can apply this value to the
rates of civilization development to see how many technologically sophisticated we would expect to find within our
The optimistic rate was 1.71 per year, and multiplying this over LG years
gives a total of 17,100,000,000 civilizations. This seems far too high - the Galaxy would be
crammed with intelligent life, with civilizations emerging around some 9% of the
Galaxy's stars. This
figure is surely too extreme be correct.
The pessimistic estimates give a figure that seems more likely, but still a remarkably high one. According
to these values, our Galaxy is host to about 4,000 technological species. If
we presume that these are spread fairly evenly through the spiral, these
would develop very roughly 1,000 light years from one another. These figures are by no means
certain, of course, and as minimal values may be rather too pessimistic. Nonetheless, they seem realistic, and go some way to
explaining why these beings are so difficult to locate: just one
star in fifty million would be host to an advanced civilization.
Assumptions Behind the Equation
Inevitably, the Drake Equation must make certain assumptions about the civilizations it attempts
to count. The accuracy of some of these assumptions will necessarily affect the outcome of the equation.
Some of the more important are listed here.
- The Use of Radio
The equation was originally formulated for use in a SETI programme designed to detect interstellar radio signals,
and assumes that any civilizations that programme might detect must be using radio themselves. This may well be
correct, but we need to consider another possibility: that there may be better means of interstellar communication
that we have yet to discover. If we could apply the principles of quantum physics, say, to transmit signals beyond
the speed of light, we would rapidly abandon radio as a communication tool. If this is possible, then it
is more than likely that any sufficiently advanced civilizations will have done the same.
This is where Drake's original L term becomes important. In its most specific sense, it describes the period
of time for which a species is open to radio detection. We need to consider the possibility that a civilization
may fall radio-silent, not because it has become extinct, but because it has developed beyond the use of radio.
This L factor is simply incalculable. Perhaps radio is the universal communication tool, and L is very high.
But, if L is small, it may be that radio-based SETI is very unlikely to succeed. Indeed, for all we know, the air might
already be thick with signals from our interstellar neighbours, waiting for us to develop the technology to receive them.
- Interstellar Travel
A second assumption underlying the equation is the idea that technological civilizations each represent a single potential source
of radio transmissions. In other words, it is assumed that each civilization is sedentary, remaining on its
home planet, or at least within the system of its home star.
This may not be the case. Even from the pessimistic calculations above, there would be about 4,000,000,000
planets suitable for life in the
Galaxy, ample incentive for a technologically advanced species to investigate actual travel
between the stars.
Interstellar travel is certainly a theoretical possibility. For species that evolve in denser regions of the
Galaxy than ours, it might even be quite practical, since the
stars in such a region would be much nearer to one another. This is
an important consideration for the Drake Equation, since each new star system 'colonised'
represents another potential radio signal. Several civilizations expanding like this over a period of millions of years might
increase the number of signals exponentially. Is this a realistic possibility, or just fanciful speculation?
There is simply no way of knowing.
- Meaningful Communication
Probably the most fundamental assumption behind the equation - and an essential one - is that we would be able
to conduct meaningful communication with any civilization we encountered, or at least interpret any
signal we might receive. This might not necessarily be the case.
Though we know nothing about any other civilizations in our Galaxy, we can deduce one fact
with considerable confidence: that the human race is by far the most primitive and undeveloped of them. Humans have been
capable of radio communication for about a century. From the calculations above, it is quite possible that the next most
advanced lifeform in the Galaxy achieved that milestone more than two
million years ago. If we ever do intercept a signal of extraterrestrial origin, there's every chance
that the sending civilization might be be tens or even hundreds of millions of years old. This isn't just
a remote possibility - the Drake Equation itself suggests that it is the most probable situation.
Consider the relationship between humans and chimpanzees. We parted company on the evolutionary
ladder about seven million years ago, and since then our technology has developed electronics while theirs
has remained at the 'twig' level. When we look back across those seven million years, we can
get some idea of how another civilization might view us. Communication would certainly be very difficult,
and indeed they might fail to recognize us as 'intelligent' at all. For such a civilization, trying to
communicate with us might be like our trying to explain relativity to a chimpanzee.
Is this a fair comparison? We can only hope not, but until we encounter a civilization millions of years beyond
our own, we can say nothing about it for sure.
Consequences of the Equation
Drake's Equation is an ingenious and powerful tool. Nobody can say how accurate it is at reaching a result,
but that isn't the true measure of its value. Its importance is that it forces us to think about the problem of
extraterrestrial civilizations in a structured and concrete way. Some of the conclusions it suggests might seem bizarre
and counter-intuitive, but this is a topic beyond any human's experience, where intutition is not a useful
The question of extraterrestrial intelligence is one without certain answers - anything and everything on this page might
be wrong. The equation brings us close to certainty on one point, though: we can be confident that
Earth is not the only living planet. Even assuming pessimistic
values for the equation's factors, it still gives us thousands of civilizations in our
Galaxy alone, and perhaps millions of other living worlds.